Zone Plate Research Articles

A Comparative Analysis of Intensity and Energy Flux in the Focus of the High-Numeric-Aperture Conventional and Spiral Zone Plates

A Comparative Analysis of Intensity and Energy Flux in the Focus of the High-Numeric-Aperture Conventional and Spiral Zone Plates

Expanding THz Vortex Generation Functionality with Advanced Spiral Zone Plates Based on Single‐Walled Carbon Nanotube Films

AbstractOptical elements based on nanomaterials are becoming major avenues to satisfy the technological requirements of compact, lightweight, and tunable elements of the emerging terahertz (THz) field. A new generation of diffractive components integrating specific geometry with additional features (flexibility, stretchability, rotation, and other approaches for tuning properties) extends the functionality of wavefront control. Here, an innovative approach is demonstrated to control the THz wavefront via a layered composition of spiral zone plates (SZPs) with tunable mutual orientation and scaling. As a proof of concept, the SZP is designed using Laguerre‐Gauss mode analysis with further fabrication and experimental characterization of the resultant vortex beams. For each single SZP, a flexible element is proposed based on a thin film of single‐walled carbon nanotubes deposited on a stretchable substrate. Thus, this diffraction element can be tuned not only by rotation (along the azimuthal direction), but also by its stretching (in the radial direction). The spatial tuning of the developed SZPs (spiral zone plates) opens up an efficient, convenient, and highly customizable approach for the manipulation of vortex beams.

Producing focused extreme ultraviolet vortex with Fermat-spiral photon sieves

Extreme ultraviolet (EUV) light is difficult to focus due to strong absorption of most materials. Photon sieves (PS), rather than Fresnel zone plates (FZP), can focus EUV to smaller spot and suppress the higher orders of secondary maxima by several orders of magnitude. The number of pinholes used in PS is far more than that of transparent rings used in FZP, providing a great flexibility to manipulate structured focusing in EUV. In this work we investigate the Fermat-spiral PS to produce focused vortices with different topological charges. Experiment at the wavelength of 46.9 nm is carried out and multi-planar coherent diffractive imaging is used to retrieve the phase map of the focused EUV vortices. These results show the enormous potential of PS for manipulating EUV light. This study not only provides a compact, affordable substitute to focusing vortices where transmissive optics materials are unavailable, but also provides a route of converting various complex light manipulation ranging from visible light to EUV and soft x-ray.

Research on the Grinding Process of Superhard Particles in the Fluidized Bed Opposed Jet Mill Based on the CFD-DEM Methodology

The process of superhard particle breakage in the grinding zone of the fluidized bed opposed jet mill is investigated using the CFD-DEM (computational fluid dynamics-discrete element method) coupling method with the Tavares UFRJ Breakage Model in the present study. The effects of structural and operational parameters, such as target plate structure, nozzle position, air inlet velocity, and feed rate, on the equipment stress distribution, airflow velocity, pressure field, particle velocity, and cumulative particle size distribution are thoroughly studied to determine the optimal structural and operational parameters. Experimental validation is conducted, including scanning electron microscope (SEM) observation of particle morphology and analysis of particle size distribution of ground product particles. The simulation results indicate that the wear rate of the structure without a target plate is lower than that of the structure with a target plate in the grinding central zone. Therefore, the structure without a target plate is chosen for further investigation. The cumulative particle size distribution after grinding is influenced by nozzle position, air inlet velocity, and feed rate. The particle D50 is positively correlated with nozzle spacing and feed rate, while it is negatively correlated with air inlet velocity. The optimal grinding effect is achieved when the distance between the nozzle and the center of the grinding zone ranges from 52.5 mm to 72.55 mm, the air inlet velocity is 950 m/s, and the feed rate is 10.5 g/s. Through experimental investigation, it has been observed that when the feed rate is 10 g/s, the particle size distribution becomes more uniform. Furthermore, consistent trends in the cumulative particle size distribution in the experiment and simulation results can be found, which validates the present numerical model. It was observed that particles at low feed rates retain certain angular edges, while particle roundness increases at high feed rates.

Enhanced imaging with binary circular Dammann Fresnel zone plate

We introduce a novel approach in optical engineering by combining Dammann gratings with binary Fresnel zone plates to create a unique hybrid optical element with enhanced energetic efficiency of its focal spots. Traditionally, binary Fresnel zone plates focus light at multiple points with varying intensities, while Dammann gratings are renowned for their efficient and uniform light splitting capabilities. Our innovation lies in merging these two elements and generating a binary circular Dammann (varying along the radial direction) Fresnel zone plate that concentrates most of the incident light into a small and desired number of focused points with equal intensities, rather than distributing light’s energy non-equally across multiple points. This novel design significantly enhances the efficiency and precision of light manipulation. It opens new possibilities in applications requiring high-intensity focal points, such as in advanced medical imaging and in accurate scientific measurements. By redefining the conventional roles of these optical elements, our research contributes an advancement to the field, paving the way for innovative solutions in various optical applications.

High‐resolution x‐ray emission spectrometry in the lithium K range with a reflection zone plate spectrometer

AbstractImplementing a newly developed spectrometer for the soft x‐ray range of (35–130) eV based on reflection zone plates was successfully accomplished on an electron probe microanalyzer. In this context, we present the first spectra acquired using this setup, including those of elements such as Be (Kα), C (Kα), Mg (L2,3), Al (L2,3), and Si (L2,3). We have also conducted an analysis of several lithium compounds and measured the emission of Li Kα from metallic Li, LiF, and LiNbO3. Some of the results were compared with density functional theory calculations. The spectrum obtained for the lithium‐bearing mineral amblygonite Li0.75Na0.25Al(PO4)F0.75(OH)0.25 is chosen to discuss some of the challenges faced.

Model-driven CT reconstruction algorithm for nano-resolution X-ray phase contrast imaging

Abstract The low-density imaging performance of a zone plate based nano-resolution hard X-ray computed tomography (CT) system can be significantly improved by incorporating a grating-based Lau interferometer. Due to the diffraction, however, the acquired nano-resolution phase signal may suffer splitting problem, which impedes the direct reconstruction of phase contrast CT (nPCT) images. To overcome, a new modeldriven nPCT image reconstruction algorithm is developed in this study. In it, the diffraction procedure is mathematically modeled into a matrix B, from which the projections without signal splitting can be generated invertedly. Furthermore, a penalized weighed least-square model with total variation (PWLS-TV) is employed to denoise these projections, from which nPCT images with high accuracy are directly reconstructed. Numerical experiments demonstrate that this new algorithm is able to work with phase projections having any splitting distances. Moreover, results also reveal that nPCT images of higher signal-to-noiseratio (SNR) could be reconstructed from projections having larger splitting distances. In summary, a novel model-driven nPCT image reconstruction algorithm with high accuracy and robustness is verified for the Lau interferometer based hard X-ray nano-resolution phase contrast imaging.

Improving soft X-ray imaging contrast uniformity of 50nm Au zone plate by optimizing pulse plating

The Fresnel zone plate plays a pivotal role in X-ray imaging systems, directly influencing the uniformity of imaging contrast. Achieving uniform imaging contrast imposes stringent requirements on the linewidth and height uniformity of the zone plate. The current mainstream method for zone plate fabrication involves utilizing electron beam lithography in conjunction with electroplating. However, in structures with large aspect ratios, precise deposition of gold to the bottom of the trench through electroplating becomes increasingly challenging to control. In this study, we employed a pulse plating process to enhance the uniformity of the plating height. Detailed investigations were conducted to analyze the effects of pulse current density, pulse duty cycle, and pulse frequency on plating height. Utilizing pulse plating, we successfully fabricated a zone plate with an outermost width of 50 nm and a thickness of approximately 245 nm. Structural analysis showed that the plating height uniformity is improved to better than 5%. The high uniformity imaging pattern was obtained by using the Siemens star test pattern at the soft x-ray imaging station at NSRL. The spatial resolution was down to 50 nm.

Experimental and numerical investigation of through-diaphragm in H-shaped steel beam to CFST column connections

This research proposes a cruciform through-diaphragm (CTD) for an H-shaped steel beam to concrete-filled steel tubular (CFST) column and investigates its seismic performance experimentally and numerically. The proposed connection consists of through-plates passing through the aligned slots in the panel zone and end plates directly welded to an H-shaped steel beam. This connection eliminates welding inside the steel tube for installation of the diaphragm, while providing a reliable load path from the steel beam to the CFST column. The experimental program examined the connection hysteretic behaviors, including the moment-rotation response, ductility, initial stiffness, and energy dissipation capacity. The proposed connection shows stable hysteric behavior and good energy dissipation up to a story drift up to 4 % and satisfies the AISC seismic provisions criteria for special moment connection. A finite element (FE) model was established and verified against the experimental results. The effects of concrete infill, steel tube column thickness, axial load ratio, and through-plate thickness on the hysteretic behavior of the proposed connection were investigated through parametric analysis of 24 FE models. This study provides the information on the optimized design parameters that ensures the stable seismic performance of the proposed connection that could be used in structural engineering practice.

High-resolution ptychographic imaging at a seeded free-electron laser source using OAM beams

Electromagnetic waves possessing orbital angular momentum (OAM) are powerful tools for applications in optical communications, quantum technologies, and optical tweezers. Recently, they have attracted growing interest since they can be harnessed to detect peculiar helical dichroic effects in chiral molecular media and in magnetic nanostructures. In this work, we perform single-shot per position ptychography on a nanostructured object at a seeded free-electron laser, using extreme ultraviolet OAM beams of different topological charge orders ℓ generated with spiral zone plates. By controlling ℓ, we demonstrate how the structural features of OAM beam profiles determine an improvement of about 30% in image resolution with respect to conventional Gaussian beam illumination. This result extends the capabilities of coherent diffraction imaging techniques, and paves the way for achieving time-resolved high-resolution (below 100 nm) microscopy on large area samples.

Utilizing the phenomenon of diffraction for noise protection of roadside objects

Abstract Presented here is a constructive solution to the challenge of utilizing the diffraction phenomenon for mitigating noise around roadside objects caused by the movement of vehicles on transportation routes. In contrast to existing prototypes, the innovation of the proposed solution lies in the creation of an active system that concentrates and directs oscillations originating from transportation sources. This active system, centered around sound absorption and reflection, establishes protective barriers and focuses on sound vibrations. The incorporation of diffraction effects within the Fraunhofer zones, along with the utilization of Fresnel lenses, directs attention towards these vibrations. The technical objective of harnessing the diffraction phenomenon for noise reduction around roadside objects involves demonstrating the feasibility of using a Fresnel zone plate (FZP) tailored for a specific oscillation frequency. This plate should demonstrate the ability to effectively manipulate sounds of varying frequencies while retaining its diffractive focusing capabilities. The intrinsic frequency characteristics of diffractive elements cannot be eliminated due to the inherent nature of sound diffraction. Consequently, it is imperative to thoroughly investigate and account for these properties. A groundbreaking discovery has been made, confirming the phenomenon of noise concentration originating from transportation sources. This revelation suggests that when a FZP is employed at frequencies other than its designed frequency, the concentration of oscillations remains. However, only the focal point of concentration shifts. Through experimentation, it has been established that the same FZP can be employed for varying wavelengths within a range of approximately ±20% while adhering to diffraction conditions. The feasibility of employing the thin lens formula to focus oscillations following the passage through a FZP has been substantiated. This solution also delves into the principal focusing, frequency, and shaping characteristics of the diffractive elements within FZPs. Furthermore, a computed estimation of the acoustic field scattered by a diffraction grating is compared against experimental data. This validates the approach and its efficacy in practical scenarios. The potential of harnessing the diffraction phenomenon to concentrate and regulate noise from transportation sources, thereby safeguarding roadside objects, is presented as a promising avenue for exploration.

Reflection imaging with a helium zone plate microscope

Neutral helium atom microscopy is a novel microscopy technique which offers strictly surface-sensitive, non-destructive imaging. Several experiments have been published in recent years where images are obtained by scanning a helium beam spot across a surface and recording the variation in scattered intensity at a fixed total scattering angle θSD and fixed incident angle θi relative to the overall surface normal. These experiments used a spot obtained by collimating the beam (referred to as helium pinhole microscopy). Alternatively, a beam spot can be created by focusing the beam with an atom optical element. However up till now imaging with a focused helium beam has only been demonstrated in transmission (using a zone plate). Here we present the first reflection images obtained with a focused helium beam (also using a zone plate). Images are obtained with a spot size (FWHM) down to 4.7μm±0.5μm, and we demonstrate focusing down to a spot size of about 1μm. Furthermore, we present experiments measuring the scattering distribution from a focused helium beam spot. The experiments are done by varying the incoming beam angle θi while keeping the beam-detector angle θSD and the point where the beam spot hits the surface fixed - in essence, a microscopy scale realization of a standard helium atom scattering experiment. Our experiments are done using an electron bombardment detector with adjustable signal accumulation, developed particularly for helium microscopy.

Dynamic Interplay: Unveiling the Biosphere-Geosphere Nexus in Carbon Cycling

A model describing the interaction of geological and biosphere processes is proposed. It is based on the postulate of the gravitational effect of the bodies of the solar system on the lithosphere plates' movement through magma flows and deep breathing of the Earth. The continuous movement of the plates consist of orogenic cycles. The cycles include a short-term orogenic periods of relatively fast plates' movement and long-term geosynclinal periods of relatively slow movement. The fast movement is caused by rifting, when magma breaks through the thin shell of the lithosphere and hardens in contact with sea water, forming a new plate. During the orogenic period, oceanic plates collide with the continental margin plate in the subduction zone. The energy of the collisions initiates thermochemical sulfate reduction, in which sedimentary organic matter (OM) is oxidized. The resulting CO2 rises to the surface of the Earth, spreads over the planet, initiating photosynthesis. In the geosynclinal period due to the slow plates' movement the released collision energy is insufficient to initiate thermochemical sulfate reduction.

Elliptical spiral zone plate fabrication using direct laser writing for generating an elliptical perfect vortex beam.

We report and fabricate a novel, to our knowledge, vortex beam generator called elliptical spiral zone plate (ESZP) using direct laser writing (DLW), which can generate the elliptical perfect vortex beam (EPVB). It is shown that the radius of the EPVB can be adjusted by tuning the control parameters of the ESZP. It is verified through the interference experiment and the Hermitian-Gaussian light field that the topological charge of the EPVB is consistent with the design. In addition, we integrate the ESZP at the tip of the single-mode fiber. Our work may set the scene for applications in fiber optical tweezers, optical communications, and integrated optics.

Recoding double-phase holograms with the full convolutional neural network

Herein, we proposed a method to recode double-phase holograms (DPHs) with a full convolutional neural network (FCN) for alleviating the fringes and spatial shifting noises in that. There are many fringes near the edge of the diffraction field due to the incomplete Fresnel zone plate, and the pixel-by-pixel encoding method of DPH will cause above fringes to appear in the reconstructed image of that as well. Besides, the spatial shifting noises generated during the conversion from complex-amplitude information to pure-phase information will also decrease the reconstruction quality and definition. Depending on the great nonlinear fitting ability of FCN, the proposed method can recode DPHs, alleviating the fringes and removing the spatial shifting noises effectively. Finally, the phase-only holograms with the resolution 2400 × 4096 have been generated in 0.06 s, which have a peak signal to noise ratio (PSNR) of 35.6 dB in the mean reconstruction quality. Optical results showed that compared with the conventional methods, the target images reconstructed by the proposed method have less noise and a higher display quality.

Optimum design of aspect ratio limited x-ray zone plates

Fresnel zone plates are widely used for nanofocusing in x-ray microscopy. The focusing performance is described in terms of the resolution, related to the width of the smallest outermost zones, and the efficiency, governed by the thickness of the zones and therefore the amount of phase shift imparted onto the x-ray beam. The ratio of zone thickness to width, or “aspect ratio,” is limited in all methods of zone plate fabrication, requiring compromises between efficiency and resolution. We propose a new zone plate design method, which optimizes focusing efficiency within a set of practical constraints. This phasor-based method is used to optimize subject to a maximum aspect ratio the design of binary, multilevel, and kinoform zone plates. A truncated zone plate profile is proposed, which focuses more efficiently than binary or kinoform zone plates, with considerably higher manufacturability. Focused ion beam milling was used to fabricate the designed lenses in gold, and their relative efficiency was validated at a synchrotron hard x-ray beamline. Our phasor method provides rapid design optimization, producing the ultimate lens designs for a given manufacturing limit, and it is fully generalizable to incorporate any fabrication tolerances such as roughness, zone displacements, and zone wall inclination.

Light Engineering and Silicon Diffractive Optics Assisted Nonparaxial Terahertz Imaging

AbstractThe art of light engineering unveils a world of possibilities through the meticulous manipulation of photonic properties such as intensity, phase, and polarization. Precision control over these properties finds application in a variety of fields spanning communications, light–matter interactions, laser direct writing, and imaging. Terahertz (THz) range, nestled between microwaves and infrared light, stands out for its remarkable ability to propagate with minimal losses in numerous dielectric materials and compounds, making THz imaging a powerful tool for noninvasive control and inspection. In this study, a rational framework for the design and optimal assembly of nonparaxial THz imaging systems is established. The research is centered on lensless photonic systems composed solely of high‐resistivity silicon‐based nonparaxial elements such as the Fresnel zone plate, the Fibonacci lens, the Bessel axicon, and the Airy zone plate, all fabricated using laser ablation technology. Through a comprehensive examination through illumination engineering and scattered light collection from raster‐scanned samples in a single‐pixel detector scheme, the imaging systems are evaluated via diverse metrics including contrast, resolution, depth of field, and focus. These findings chart an exciting course toward the development of compact and user‐friendly THz imaging systems where sensors and optical elements seamlessly integrate into a single chip.

Experimental study on subwavelength focusing optical field detection methods for micro-Fresnel zone plate

In this paper, the detection methods and detection systems for the subwavelength focusing optical field of the micro-Fresnel zone plate (FZP) are experimentally studied. First, a comparison is made between the micro/nanofabrication methods for micro-FZP, namely, focused ion beam (FIB) and electron beam lithography, and the results show that FIB is better suited for the amplitude-type micro-FZP fabrication. Subsequently, the experimental detection devices based on the wide-field microscopy amplification (WFMA) imaging method (indirect detection method) and scanning near-field optical microscopy (direct detection method) are, respectively, constructed for the detection of the subwavelength focusing optical field of micro-FZP. The experimental results are compared and analyzed with theoretical calculation results, indicating that the WFMA method is more suitable for the detection of micro-FZP subwavelength focusing optical field that is not sensitive to radial components. This study provides an experimental reference for the micro/nanofocusing optical field detection of micro/nano-optical components similar to micro-FZP and promotes the practical application of micro-FZP.

Generation of ultra-intense vortex laser from a binary phase square spiral zone plate.

With the development of ultra-intense laser technology, the manipulation of relativistic laser pulses has become progressively challenging due to the limitations of damage thresholds for traditional optical devices. In recent years, the generation and manipulation of ultra-intense vortex laser pulses by plasma has attracted a great deal of attention. Here, we propose a new scheme to produce a relativistic vortex laser. This is achieved by using a relativistic Gaussian drive laser to irradiate a plasma binary phase square spiral zone plate (BPSSZP). Based on three-dimensional particle-in-cell (3D-PIC) simulations, we find that the drive laser has a phase difference of π after passing through the BPSSZP, ultimately generating the vortex laser with unique square symmetry. Quantitatively, by employing a drive laser pulse with intensity of 1.3 × 1018~W/cm2, a vortex laser with intensity up to 1.8 × 1019~W/cm2, and energy conversion efficiency of 18.61% can be obtained. The vortex lasers generated using the BPSSZP follow the modulo-4 transmutation rule when varying the topological charge of BPSSZP. Furthermore, the plasma-based BPSSZP has exhibited robustness and the ability to withstand multiple ultra-intense laser pulses. As the vortex laser generated via the BPSSZP has high intensity and large energy conversion efficiency, our scheme may hold potential applications in the community of laser-plasma, such as particles acceleration, intense high-order vortex harmonic generation, and vortex X/γ-ray sources.

Generation of a sub-wavelength optical needle by wavelength shifting and center masking of a Fresnel zone plate

In this paper, a method to generate a sub-wavelength optical needle is proposed and demonstrated by wavelength shifting and center masking in the Fresnel zone plate (FZP). In theory, the vectorial angular spectrum (VAS) theory combined with genetic algorithm (GA) is used for the design of the center-masking FZP for generating optical needle, and finite-difference time-domain (FDTD) method is used for theoretical validation. In experiment, an amplitude-type center-masking FZP with a processing error of 5 nm is fabricated by focused ion beam etching (FIB), and the focusing intensity distribution of the optical needle is measured based on a self-made device. Finally, a sub-wavelength optical needle in far field is obtained, featuring a depth of focus of 7.16 µm, a central focal length of 26.87 µm, and a minimum full width at half maximum of 500 nm and 467 nm in x and y directions, respectively. This study provides both theoretical and experimental foundations for the practical application of FZPs.